Molecular dynamic simulation of the crystallization of liquid iron nanoparticles

148 JOURNAL OF SCIENCE OF HNUE DOI: 10.18173/2354-1059.2017-0043 Mathematical and Physical Sci. 2017, Vol. 62, Iss. 8, pp. 148-155 This paper is available online at MOLECULAR DYNAMIC SIMULATION OF THE CRYSTALLIZATION OF LIQUID IRON NANOPARTICLES Nguyen Thi Thao1 and Le Van Vinh 2 1 Faculty of Physics, Hanoi National University of Education 2 School of Engineering Physics, Hanoi University of Science and Technology Abstract. The crystallization of liquid iron nanoparticles has been investigated by means of molecular dynamic (MD) simulation. The simulation result shows that when the liquid iron samples are cooled from 2500 K to 300 K at a cooling rate of 0.667 K/ps, they are crystallized into body centered cubic (BCC) phase. The transformation to crystalline phase was analyzed using the Common Neighbor Analysis (CNA) method. It was shown that the crystallization proceeds through two processes. The first process is the transition from a liquid to an icosahedrons (ICO) structure. The other is a transition from an ico to bcc structure. The structural transformation depends on the size of the liquid iron nanoparticles. Keywords: Crystallization, liquid iron nanoparticles, phase transition, common neighbor analysis (CNA), molecular dynamics (MD). 1. Introduction Nanoparticles can be produced in both crystalline and amorphous states by means of reasonable synthesis methods [1, 2]. Generally, the amorphous state is thermally unstable and amorphous nanoparticles can be crystallized under thermal annealing. The crystallization process may also occur when a sample is cooled using a reasonable cooling rate. It was found that the crystallization temperatures of amorphous nanoparticles are size dependent [3, 4]. A study of the size and temperature dependence of the nucleation rates of Fe nanoparticles with a size of 1436 and 2133 atoms crystallized from liquid in the temperature range of 750 - 1160 K was carried out [5]. The MD results confirmed that the sizes of critical nuclei decrease with increases in the degree of supercooling, and the nucleation rate increases initially as the degree of supercooling increases.A study has been done on liquid gold nanoparticles based on the modified embedded-atom-method potential [6]. It was found that with a decreasing cooling rate, the final structure of the particle changes from amorphous to crystalline via an icosahedron-like structure. However, the atomic mechanism of crystallization in liquid iron nanoparticles is still poorly understood. Therefore, in this work the crystallization mechanism and intermediate phases of liquid iron nanoparticles are investigated using the Common Neighbor Analysis (CNA) method. This analysis method helps to recognize perfect crystal structures and differentiate structural defects [7]. To evaluate the effects of size of nanoparticle samples on their crystallization, we have prepared three nanoparticle samples with the size of 1458, 3456, and 5880 atoms and a bulk sample. Received June 23, 2017. Accepted August 15, 2017. Contact Nguyen Thi Thao, email: ntthao.hnue@gmail.com Molecular dynamic simulation of the crystallization of liquid iron nanoparticles 149 2. Content 2.1. Calculation procedure A molecular dynamics (MD) simulation was conducted to study liquid iron nanoparticles. The Pak–Doyama potential [8] was used to describe the inter-atomic potential between Fe atoms. The MD simulation was performed for three samples of Fe nanoparticles containing 1458 atoms (S1) , 3456 atoms (S2) and 5880 atoms (S3) with free boundary conditions. The three samples were built as a body centered cubic crystal structure. They were placed in a box-shaped simulation space that is eight times larger than the size of nanoparticle samples. The MD step is equal to 1.5 fs. Three samples of Fe nanoparticles were heated from 300 K to 2500 K at 4 K / ps. After these samples reached 2500 K, they were maintained at this temperature for a period of 100 ps. These samples were then cooled to 300 K with a cooling rate of 0.667 K/ps to study their crystallization. 2.2. Results and discussion Figure 1 shows the temperature dependence of mean potential energy per atom of nanoparticle and bulk samples. This energy decreases when temperature increases. However, we observe that the potential energy of nanoparticle samples S2, (S3) and the bulk sample were suddenly reduced at temperatures of 965, 1000 and 1096 K, respectively. This result indicates that there is a structural transformation in these samples. For sample S1, we don't observe a sudden change of energy during the decrease of temperature. So, there is no structural transformation in sample S1. 400 600 800 1000 1200 1400 1600 1800 -3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 P E (e V /a to m ) Temperature(K) 1458 atoms 3456 atoms 5880 atoms bulk Important information concerning the Fe crystal can be derived from the radial distribution function (RDF). In Fig.2, we present RDF of nanoparticle and bulk samples at 300 K. It is clear that the RDF of samples S2, S3 and the bulk sample represent the order of the crystal material, whereas the radial distribution function of sample S1 represents the structure of the amorphous Fig.1. The temperature dependence of mean potential energy per atom of nanoparticle and bulk samples. Nguyen Thi Thao and Le Van Vinh 150 material. Thus, crystallization does not occur with a small nanoparticle sample with the size of 1458 atoms, which occurs with larger sized nanoparticle and bulk samples. For a detailed explanation of the structure of these samples, we used a common neighbor analysis (CNA) method. With the CNA method, we found samples containing both icosahedrons (ICO) and body centered cubic (BCC) structures during cooling. Fig. 3 shows the clusters of ico and bcc structures of samples during cooling. As shown in Fig. 3, ico clusters are formed in the range of temperature from 1600 K to 1100 K. Crystal cluster does not appear in sample S1. The bcc crystal clusters appear in samples S2, S3 and the bulk sample at temperatures of 1000 K, 1000 K and 1060K, respectively. Nic and Nbico respectively are the number of ico clusters and the number of atoms of the biggest ico cluster. 2 4 6 8 0 2 4 6 8 10 12 bulk S3 S2 S1 G (r ) r(Å) Fig. 2. The RDF of nanoparticle and bulk samples at 300 K after cooling at a cooling rate of 0.667 K/ps. The temperature dependence of Nic and Nbico nanoparticles and bulk samples are listed in Table 1. When the temperature decreases, the number of ico clusters of Nic increases to a maximum value at 1100 K for samples S1 and S2, and at 1200 K for sample S3 and the bulk sample. However, when the temperature decreases to 900 K, Nic decreases rapidly. The number of atoms of the largest ico cluster (Nbico) increases as temperature decreases. This result shows that ico clusters grow and they are grouped together into a structure cluster. Nic is equal to 2 at 900 K for sample S1. Meanwhile, it is equal to 0 for samples S2, S3 and the bulk sample due to the structural transformation from ico to bcc phase. We divide nanoparticle samples into spherical layers with a thickness of 2 × a0 (a0 is the lattice constant which equals 2.856 Å). The center of these spheres is the centef of mass of the nanoparticles as schematically illustrated in Fig. 4. Here nanoparticles are divided into four layers. In Table 2, we show the mean potential energy per atom, the number of liquid atoms (nli), the number of ico atoms (nico) and the number of bcc atoms (ncry) in each layer. Molecular dynamic simulation of the crystallization of liquid iron nanoparticles 151 Fig. 3. Clusters of ico and bcc structures of nanoparticles and bulk samples at determined temperatures during cooling Table 1. The number of ICO clusters (Nic) and the number of atoms of the largest ICO cluster (Nbico) of nanoparticles and bulk samples T(K) S1 S2 S3 Bulk Nic Nbico Nic Nbico Nic Nbico Nic Nbico 1600 5 25 7 19 17 25 17 25 1500 6 31 16 28 25 21 18 55 1400 9 31 15 51 31 38 21 59 1300 11 39 26 67 38 44 33 72 1200 11 70 28 86 59 55 35 77 1100 16 75 39 98 51 126 34 258 1000 7 318 24 1018 23 245 0 0 900 2 894 0 0 0 0 0 0 Nguyen Thi Thao and Le Van Vinh 152 Fig. 4. Schematic illustration of spherical layers of nanoparticle Table 2. The main characteristics of each layer of nanoparticles. Here (PEli), (PEico), (PEcry) are the mean potential energy per atom of liquid , ICO and BCC atom, respectively (eV/atom); (nli), (nico), (ncry) is the number of liquid, ICO and BCC atoms of each layer, respectively a) S1 L ay er 1900K 1600K 1100K 1000K P E  l i P E  i co n li /n ic o P E  l i P E  i co n li /n ic o P E  l i P E  i co n li /n ic o P E  l i P E  i co P E  c ry n li /n ic o /n cr y 1 -2 .1 4 6 - 5 9 /0 -2 .2 6 6 -2 .5 7 0 5 0 /8 -2 .5 3 3 -2 .6 0 7 3 0 /3 6 -2 .5 5 7 -2 .6 6 6 - 4 2 /2 1 /0 2 -2 .0 3 8 -2 .3 6 5 3 8 5 /1 5 -2 .1 8 6 -2 .4 5 6 4 0 3 /1 8 -2 .5 0 6 -2 .5 7 7 2 8 0 /1 4 6 -2 .4 8 2 -2 .5 9 0 - 2 5 0 /1 9 4 /0 3 -1 .5 7 0 -2 .0 6 3 7 5 4 /2 2 -1 .7 4 1 -2 .0 3 6 8 0 5 /6 0 -1 .9 4 0 -2 .3 4 4 6 1 9 /2 9 9 -1 .9 9 2 -2 .3 6 0 - 5 8 1 /3 4 0 /0 4 -0 .6 3 1 - 2 3 2 /0 -0 .8 8 2 - 1 1 4 /0 -1 .1 8 7 - 4 8 /0 -1 .1 1 1 -1 .6 4 8 - 2 9 /1 /0 Molecular dynamic simulation of the crystallization of liquid iron nanoparticles 153 b) S2 L ay er 1900K 1600K 1100K 1000K P E  l i P E  i co n li /n ic o P E  l i P E  i co n li /n ic o P E  l i P E  i co n li /n ic o P E  l i P E  i co P E  c ry n li /n ic o /n cr y 1 -2 .1 6 4 - 5 7 /0 -2 .1 2 5 - 6 1 /0 -2 .5 2 7 -2 .7 0 9 5 8 /1 -2 .4 8 3 -2 .5 9 6 -2 .7 0 9 1 4 /4 9 /3 2 -1 .9 7 9 -2 .2 6 2 3 4 9 /4 5 -2 .1 8 1 -2 .3 2 9 3 7 4 /2 8 -2 .4 9 0 -2 .5 4 4 2 9 8 /1 4 0 -2 .3 8 9 -2 .5 5 5 -2 .6 3 2 1 5 7 /2 2 7 /5 3 3 -2 .0 1 1 -2 .0 6 9 1 0 6 9 /9 -2 .1 8 5 -2 .4 4 0 1 0 8 8 /4 5 -2 .4 6 0 -2 .5 3 1 7 2 7 /3 4 6 -2 .5 2 9 -2 .6 3 7 -2 .7 0 5 5 0 2 /6 3 0 /5 4 4 -1 .5 8 9 -2 .1 8 5 1 4 0 8 /1 0 -1 .7 8 1 -2 .1 6 7 1 5 6 9 /2 5 -1 .9 8 0 -2 .3 5 7 1 3 1 6 /4 4 7 -1 .9 7 5 -2 .3 8 1 -2 2 .4 2 4 1 0 2 0 /6 9 3 /1 1  5 - 0 .6 2 8 - 5 0 9 /0 -0 .8 6 0 - 2 6 6 /0 -1 .0 1 9 -1 .3 1 4 1 2 3 /1 -1 .2 5 4 -1 .4 5 4 - 4 3 /2 /0 At 1900 K, as observed in Table 2, we see that small clusters of ICO atoms are formed in the middle layers and clusters do not occur in both the inner and outer layer. When the temperature drops to 1100 K, the number of ico atoms increases and they appear almost on all layers except the outer layer. At 1000 K, the ICO atoms appear on all layers. Crystal atoms do not appear in sample S1, while they are formed from the core to the surface for nanoparticle samples S2 and S3. We also observe that the mean potential energy of different types of atoms decreases in the following orders: liquid atom (PEli) → ico atom (PEico) → bcc atom (PEcry). Nguyen Thi Thao and Le Van Vinh 154 c) S3 L ay er 1900K 1600K 1100K 1000K P E  l i P E  i co n li /n ic o P E  l i P E  i co n li /n ic o P E  l i P E  i co n li /n ic o P E  l i P E  i co P E  c ry n li /n ic o /n cr y 1 -1 .9 3 7 - 5 6 /0 -2 .2 2 4 - 5 7 /0 -2 .4 9 3 -2 .4 9 8 5 0 /9 - - -2 .7 3 6 0 /0 /6 6 2 -2 .0 4 7 - 3 9 7 /0 -2 .2 0 9 -2 .4 2 7 3 9 8 /2 5 -2 .4 7 8 -2 .5 2 7 2 6 7 /1 7 6 -2 .5 3 9 -2 .6 1 4 -2 .7 0 5 3 5 4 /1 3 /8 0 3 -2 .0 3 8 -2 .0 4 4 1 0 6 6 /1 1 -2 .2 1 1 -2 .3 2 7 1 0 4 9 /6 0 -2 .4 6 3 -2 .5 5 6 6 9 4 /4 7 2 -2 .5 2 7 -2 .6 1 3 -2 .7 0 6 2 9 6 /1 9 5 /7 2 0 4 -1 .9 3 8 -2 .1 6 3 2 0 4 5 /3 6 -2 .1 7 5 -2 .3 3 0 2 0 1 6 /1 6 4 -2 .4 4 7 -2 .5 7 7 1 5 6 5 /7 3 7 -2 .5 1 5 -2 .6 1 5 -2 .6 6 0 7 1 3 /6 6 9 /9 6 9 5 -1 .4 7 9 -2 .2 6 7 1 7 6 0 /5 -1 .6 0 6 -2 .0 2 0 1 8 8 4 /5 0 -1 .8 5 1 -2 .2 2 5 1 5 8 3 /3 2 7 -1 .8 3 0 -2 .2 0 4 -2 .2 6 0 1 1 7 8 /3 8 5 /2 4 0  6 - 0 .6 0 8 - 5 0 4 /0 -0 .5 0 1 - 1 7 7 /0 -0 .6 0 9 - 6 /0 -1 .0 8 8 - - 2 /0 /0 Molecular dynamic simulation of the crystallization of liquid iron nanoparticles 155 Thus, the cooling of liquid Fe nanoparticle samples from 2500 K to 300 K with a cooling rate of 0.667 K / ps shows a structural transformation in the nanoparticles. Sample S1 has the transition only from a liquid to ico structure. For S2, S3 and bulk samples have two structural transformations, first transform the structure from liquid to ico structure and second transform from an ico to bcc structure. The transition from liquid to ico structure takes place in large range of temperatures (from 1900 K to 1000 K), whereas the transition from ico to bcc structure takes place in narrow range of temperature (from 1000 K to 900 K). In the case of iron the icosahedral structure was found by ab initio calculations for very small clusters ranging from 11 to 15 atoms [9]. This has been confirmed by recent experimental investigations showing that iron with the size of 13 atoms has an icosahedral structure [10]. 3. Conclusion In this paper, crystallization of liquid iron nanoparticles has been investigated by means of MD simulation. The structural transformation to a crystalline phase was analyzed using potential energy and the radial distribution function. 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